The discrete divergence-free property in the VEM has been firstly
analyzed
in [1]}, [2]}
(see also [3]}) in the
framework of the Stokes and Navier-Stokes problems.
Later, it has been extended to other fluid flow models, a short list
of representatives
being [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}.
On the other hand, De-Rahm complexes in the virtual element setting
have been introduced in [18]}
and then improved (and applied to the analysis of magnetostatic
problems) in
[19]}, [20]}, [21]}.
The Maxwell's equations were the target
of [22]},
see also [23]}, [24]}, and their analysis hinges upon
technical tools from [25]}. Other
interesting results along these directions are contained
in [26]} that paves the way for a VEM discretization
of the Bianchi-Einstein equations.
